91 citations · 105 across the 8 of their papers we have counts for
7 papers · 1 filter
Analysis of a cross-diffusion model for rival gangs interaction in a city
Alethea B. T. Barbaro, Nancy Rodriguez, Havva Yoldaş +1
We study a two-species cross-diffusion model that is inspired by a system of convection-diffusion equations derived from an agent-based model on a two-dimensional discrete lattice.…
Relaxation by nonlinear diffusion enhancement in a two-dimensional cross-diffusion model for urban crime propagation
Nancy Rodriguez, Michael Winkler
We consider a class of macroscopic models for the spatio-temporal evolution of urban crime, as originally going back to Short et al. (Math. Mod. Meth. Appl. Sci. 18, 2008). The foc…
On the global existence and qualitative behavior of one-dimensional solutions to a model for urban crime
Nancy Rodriguez, Michael Winkler
We consider the no-flux initial-boundary value problem for the cross-diffusive evolution system \begin{eqnarray*} \left\{ \begin{array}{ll} u_t = u_{xx} - χ\big(\frac{u}{v} \partia…
Analysis of a model for the dynamics of riots
Henri Berestycki, Nancy Rodriguez
This paper is concerned with modeling the dynamics of social outbursts of activity, such as protests or rioting activity. In this sequel to our work in \cite{Berestycki2014}, writt…
A model of riots dynamics: shocks, diffusion and thresholds
Henri Berestycki, Jean-Pierre Nadal, Nancy Rodriguez
We introduce and analyze several variants of a system of differential equations which model the dynamics of social outbursts, such as riots. The systems involve the coupling of an…
Traveling Wave Solutions in a Reaction-Diffusion Model for Criminal Activity
Henri Berestycki, Nancy Rodriguez, Lenya Ryzhik
We study a reaction-diffusion system of partial differential equations, which can be taken to be a basic model for criminal activity. We show that the assumption of a populations n…
Inhomogeneous Patlak-Keller-Segel models and Aggregation Equations with Nonlinear Diffusion in $\Real^d$
Jacob Bedrossian, Nancy Rodriguez
Aggregation equations and Patlak-Keller-Segel (PKS) models for chemotaxis with nonlinear diffusion are popular models for nonlocal aggregation phenomenon and are a source of a numb…